The Erwin Schrr Odinger International Institute for Mathematical Physics Noncommutative Lattices and Their Continuum Limits Noncommutative Lattices and Their Continuum Limits

The Erwin Schrr Odinger International Institute for Mathematical Physics Lattices and Their Continuum Limits Lattices and Their Continuum Limits

We address the problem of the continuum limit for a system of Hausdorr lattices (namely lattices of isolated points) approximating a topological space M. The correct framework is that of projective systems. The projective limit is a universal space from which M can be recovered as a quotient. We dualize the construction to approximate the algebra C(M) of continuous functions on M. In a companio...

The Erwin Schrr Odinger International Institute for Mathematical Physics K{theory of Noncommutative Lattices K-theory of Noncommutative Lattices

Noncommutative lattices have been recently used as nite topological approximations in quantum physical models. As a rst step in the construction of bundles and characteristic classes over such noncommutative spaces, we shall study their K-theory. We shall do it algebraically, by studying the algebraic K-theory of the associated algebras of`continuous functions' which turn out to be noncommutati...

The Erwin Schrr Odinger International Institute for Mathematical Physics Noncommutative 3-sphere: a Model of Noncommutative Contact Algebras Noncommutative 3-sphere: a Model of Noncommutative Contact Algebras

The Erwin Schrr Odinger International Institute for Mathematical Physics Quasifree Second Quantization and Its Relation to Noncommutative Geometry Quasifree Second Quantization and Its Relation to Noncommutative Geometry

Schwinger terms of current algebra can be identiied with nontrivial cyclic cocycles of a Fredholm module. We discuss its temperature dependence. Similar anomalies may occur also in spin systems. In simple examples already an operator{valued cocycle shows up.

Noncommutative Lattices and Their Continuum Limits

We consider finite approximations of a topological space M by noncommutative lattices of points. These lattices are structure spaces of noncommutativeC∗-algebras which in turn approximate the algebra C(M) of continuous functions on M . We show how to recover the space M and the algebra C(M) from a projective system of noncommutative lattices and an inductive system of noncommutative C∗-algebras...